Compensatory Fitness Interaction

Compare double-mutant fitness with a multiplicative single-mutant expectation and observed rescue of the first mutation.

Description

Compare double-mutant fitness with a multiplicative expectation and test whether it exceeds the first mutant.

Epistasis describes an interaction between mutations whose combined fitness differs from an expectation based on their separate effects. The chosen expectation matters: a multiplicative reference predicts combined relative effects by multiplying the two single-mutant effects.^[1]

All four fitness measurements must share an assay, environment, and scale. Wild-type fitness sets the reference and must be positive; mutant fitness values may be zero. The tool reports an expected double-mutant fitness and a signed excess in the same fitness units.

Its rescue flag asks only whether the measured double mutant has greater fitness than the first single mutant. Positive interaction excess and rescue are separate comparisons; neither establishes statistical significance or a molecular mechanism.

When to use Compensatory Fitness Interaction

Use it to summarize a four-genotype experiment when a multiplicative fitness reference is appropriate. Keep the first mutation consistently designated if its rescue is the comparison of interest.

How to use Compensatory Fitness Interaction and interpret its calculation

Enter wildTypeFitness, firstMutationFitness, secondMutationFitness, and doubleMutationFitness using comparable measurements.
Run the calculation and compare the observed double fitness with multiplicativeExpectedFitness.
Read interactionExcess as a signed difference and rescuesFirstMutation as a strict comparison with the first mutant. Review replicate uncertainty separately.

expected = F1 × F2 / Fwild; excess = Fdouble − expected; rescue = Fdouble > F1

Dividing by wild-type fitness converts the product back to the original fitness scale.

A positive excess lies above the multiplicative reference; a negative excess lies below it. The rescue flag does not require the first mutation to be deleterious relative to wild type, and it does not require the double mutant to regain wild-type fitness.

json

{
  "input": {
    "wildTypeFitness": 1,
    "firstMutationFitness": 0.5,
    "secondMutationFitness": 0.8,
    "doubleMutationFitness": 0.7
  },
  "output": {
    "multiplicativeExpectedFitness": 0.4,
    "interactionExcess": 0.3,
    "rescuesFirstMutation": true
  }
}

Equal double and first fitness gives rescue false. A zero single-mutant fitness makes the multiplicative expectation zero. Rescaling every measurement by the same positive factor rescales the expectation and excess but leaves the rescue comparison unchanged.

Limitations and assumptions

The calculation accepts any finite nonnegative mutant fitness, including values above wild type. It does not classify mutations as harmful or beneficial in advance.

No replicate fitting, uncertainty interval, statistical interaction test, growth-curve normalization, competition correction, or mechanistic inference is performed. An assay-specific fitness measurement cannot automatically be transferred to another environment.

Alternative or Complementary methods

Normalize fitness measurements consistently before applying an interaction reference. Drug-dose interaction models use different quantities and assumptions; a dose isobole score should not be substituted for a genetic fitness interaction.

References

The contribution of epistasis to the architecture of fitness in an RNA virus (Sanjuán, Moya, and Elena, 2004) — Proceedings of the National Academy of Sciences

Similar or alternative tools

Relative Fitness
Normalize survived-offspring counts to a supplied population maximum when that is the intended fitness measure.
Isobologram Analysis
Compare two-agent dose pairs with a dose-addition reference for a different interaction question.